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Simplifying 9x2 + 14x = 2 Reorder the terms: 14x + 9x2 = 2 Solving 14x + 9x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 14x + 9x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 14x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 1.555555556x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 1.555555556x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 1.555555556x + x2 = 0 + 0.2222222222 1.555555556x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 1.555555556x + x2 = 0.2222222222 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 0.2222222222 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 0.2222222222 + 0.6049382720 Combine like terms: 0.2222222222 + 0.6049382720 = 0.8271604942 0.6049382720 + 1.555555556x + x2 = 0.8271604942 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 0.8271604942 Calculate the square root of the right side: 0.909483642 Break this problem into two subproblems by setting (x + 0.777777778) equal to 0.909483642 and -0.909483642.Subproblem 1
x + 0.777777778 = 0.909483642 Simplifying x + 0.777777778 = 0.909483642 Reorder the terms: 0.777777778 + x = 0.909483642 Solving 0.777777778 + x = 0.909483642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 0.909483642 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 0.909483642 + -0.777777778 x = 0.909483642 + -0.777777778 Combine like terms: 0.909483642 + -0.777777778 = 0.131705864 x = 0.131705864 Simplifying x = 0.131705864Subproblem 2
x + 0.777777778 = -0.909483642 Simplifying x + 0.777777778 = -0.909483642 Reorder the terms: 0.777777778 + x = -0.909483642 Solving 0.777777778 + x = -0.909483642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -0.909483642 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -0.909483642 + -0.777777778 x = -0.909483642 + -0.777777778 Combine like terms: -0.909483642 + -0.777777778 = -1.68726142 x = -1.68726142 Simplifying x = -1.68726142Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.131705864, -1.68726142}
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